12 hour to 24 hour time converter

MATL, 4 bytes

15XO

Try it online!

Explanation

Built-in function: date string conversion with automatic detection of input format and with output format 15, which corresponds to 'HH:MM'. This is equivalent to @StewieGriffin's Octave answer.

Octave, 21 17 bytes

Saved 4 bytes thanks to Luis Mendo. I could specify format number 15 instead of 'HHMM'.

@(c)datestr(c,15)

Explanation:

This is an anonymous function taking a string c as input on the format: '11:34 AM'. datestr recognizes the format automatically as one of the standard date formats, and outputs it in the specified format number 15, which is HH:MM.

Since the specified output format doesn't have AM or PM Octave automatically converts it to what you refer to as Military time.

Try it online.

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A version not using datestr using 35 bytes

@(c)[c(1:4)+[1,2,0,0]*(c(5)>97),'']

Explanation:

Takes an input string c on the format 1134am.

@(c)                              % Anonymous function
[c(1:4)                           % First 4 elements of the string
       +[1,2,0,0]                 % Add 1 and 2 to the first to the ASCII-value of the 
                                    first two characters
                 *)c(5)>97)       % if the fifth element is larger than 97 
                                    (the ASCII code for `a`).
                            ,'']  % Implicitly convert to string

Or, a different approach for 37 bytes:

@(c)[c(1:4)+('1200'-48)*(c(5)>97),'']

V, 21 17 bytes

Thanks @DJMcMayhem for 4 bytes!

í12:/0:
çp/12
$x

Try it online! This takes the format HH:MMx where x is either a or p, and returns it in the format HH:MM

Hexdump:

00000000: ed31 323a 2f30 3a0a e770 2f31 3201 2478  .12:/0:..p/12.$x
00000010: 0ae7 612f 2478                           ..a/$x

Explanation:

í12:/0:   | find and replace 12: with 0: (to avoid replacing HH:12)
ç         | on every line
 p/       | that contains a p
   12^A   | increment 12 times (the first number, hours)
$x        | delete the character at the end of the line